Harmonic entropy: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>~~2014~~-07-~~06 15~~:19:39 UTC</tt>.

: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2015-08-21 00:13:29 UTC</tt>.

: The original revision id was <tt>~~515672922~~</tt>.

: The original revision id was <tt>557087005</tt>.

: The revision comment was: <tt></tt>

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* The appearance of a quick fluttering effect sometimes known as **periodicity buzz**

~~All of these~~ effects ~~share two common characteristics~~ for ~~chords played~~ with ~~harmonic timbres:~~

These effects do not always appear strictly in tandem with one another. For instance, Paul Erlich has noted that most models for beatlessness measure 10:12:15 and 4:5:6 as being identical, whereas the latter yields exhibits more timbral fusion and a more salient virtual fundamental than the former. However, suppose we want to come up with a combined measure for how often effects such as the above tend to occur. It is then useful to note that

* ~~they~~ tend to appear most strongly for those chords with large subsets that correspond to simple chunks of the harmonic series

* effects such as these tend to appear most strongly for those chords with large subsets that correspond to simple chunks of the harmonic series

* the effects produced exhibit some degree of tolerance for mistuning

~~As the presence or absence of these effects tend~~ to ~~appear in tandem and are highly correlated with one another, we can~~ speak of a general notion of the psychoacoustic **concordance** of an interval - the degree to which effects such as the above will appear when an arbitrary musical chord is played. Additionally, chords which are very inharmonic often exhibit a quality known as psychoacoustic **discordance**.

This enables us to speak of a general notion of the psychoacoustic **concordance** of an interval - the degree to which effects such as the above will appear when an arbitrary musical chord is played. Additionally, chords which are very inharmonic often exhibit a quality known as psychoacoustic **discordance**.

While psychoacoustic concordance is not a feature universal to all styles of music, it has been utilized significantly in Western music in the study of intonation. For instance, flexible-pitch ensembles operating within 12-EDO, such as barbershop quartets and string ensembles, will often adjust intonationally from the underlying 12-EDO reference to maximize the concordance of individual chords. Indeed, the entire history of Western tuning theory -- from meantone temperament, to the various Baroque well-temperaments, to 12-EDO itself, to the modern [[@xenharmonic/Regular Temperaments|theory of regular temperament]] -- can be seen as an attempt to reason mathematically about how to generate manageable tuning systems that will maximize concordance and minimize discordance.

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The general workings of the human auditory system lead to a plethora of well-documented and sonically interesting phenomena that can occur when a musical chord is played:

<ul><li>The perception of partial timbral fusion of the chord into one complex sound</li><li>The appearance of a virtual fundamental pitch in the bass</li><li>Timbral beatlessness, compared to mistunings of the chord in the surrounding area</li><li>The appearance of a quick fluttering effect sometimes known as periodicity buzz</li></ul>

~~All of these~~ effects ~~share two common characteristics~~ for ~~chords played~~ with ~~harmonic timbres:~~

These effects do not always appear strictly in tandem with one another. For instance, Paul Erlich has noted that most models for beatlessness measure 10:12:15 and 4:5:6 as being identical, whereas the latter yields exhibits more timbral fusion and a more salient virtual fundamental than the former. However, suppose we want to come up with a combined measure for how often effects such as the above tend to occur. It is then useful to note that

<ul><li>~~they~~ tend to appear most strongly for those chords with large subsets that correspond to simple chunks of the harmonic series</li><li>the effects produced exhibit some degree of tolerance for mistuning</li></ul>

~~As the presence or absence of these effects tend~~ to ~~appear in tandem and are highly correlated with one another, we can~~ speak of a general notion of the psychoacoustic concordance of an interval - the degree to which effects such as the above will appear when an arbitrary musical chord is played. Additionally, chords which are very inharmonic often exhibit a quality known as psychoacoustic discordance.

<ul><li>effects such as these tend to appear most strongly for those chords with large subsets that correspond to simple chunks of the harmonic series</li><li>the effects produced exhibit some degree of tolerance for mistuning</li></ul>

This enables us to speak of a general notion of the psychoacoustic concordance of an interval - the degree to which effects such as the above will appear when an arbitrary musical chord is played. Additionally, chords which are very inharmonic often exhibit a quality known as psychoacoustic discordance.

While psychoacoustic concordance is not a feature universal to all styles of music, it has been utilized significantly in Western music in the study of intonation. For instance, flexible-pitch ensembles operating within 12-EDO, such as barbershop quartets and string ensembles, will often adjust intonationally from the underlying 12-EDO reference to maximize the concordance of individual chords. Indeed, the entire history of Western tuning theory -- from meantone temperament, to the various Baroque well-temperaments, to 12-EDO itself, to the modern <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Regular%20Temperaments" target="_blank">theory of regular temperament</a> -- can be seen as an attempt to reason mathematically about how to generate manageable tuning systems that will maximize concordance and minimize discordance.

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2014-07-06 15:19:39 UTC</tt>.<br>
+: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2015-08-21 00:13:29 UTC</tt>.<br>
-: The original revision id was <tt>515672922</tt>.<br>
+: The original revision id was <tt>557087005</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 20: / Line 20: @@
 * The appearance of a quick fluttering effect sometimes known as **periodicity buzz**
-All of these effects share two common characteristics for chords played with harmonic timbres:
+These effects do not always appear strictly in tandem with one another. For instance, Paul Erlich has noted that most models for beatlessness measure 10:12:15 and 4:5:6 as being identical, whereas the latter yields exhibits more timbral fusion and a more salient virtual fundamental than the former. However, suppose we want to come up with a combined measure for how often effects such as the above tend to occur. It is then useful to note that
-* &lt;span style="line-height: 1.5;"&gt;they tend to appear most strongly for those chords with large subsets that correspond to simple chunks of the harmonic series&lt;/span&gt;
+* &lt;span style="line-height: 1.5;"&gt;effects such as these tend to appear most strongly for those chords with large subsets that correspond to simple chunks of the harmonic series&lt;/span&gt;
 * &lt;span style="line-height: 1.5;"&gt;the effects produced exhibit some degree of tolerance for mistuning&lt;/span&gt;
-As the presence or absence of these effects tend to appear in tandem and are highly correlated with one another, we can speak of a general notion of the psychoacoustic **concordance** of an interval - the degree to which effects such as the above will appear when an arbitrary musical chord is played. Additionally, chords which are very inharmonic often exhibit a quality known as psychoacoustic **discordance**.
+&lt;span style="line-height: 1.5;"&gt;This enables us to speak of a general notion of the psychoacoustic &lt;/span&gt;**&lt;span style="line-height: 1.5;"&gt;concordance&lt;/span&gt;**&lt;span style="line-height: 1.5;"&gt; of an interval - the degree to which effects such as the above will appear when an arbitrary musical chord is played. Additionally, chords which are very inharmonic often exhibit a quality known as psychoacoustic &lt;/span&gt;**&lt;span style="line-height: 1.5;"&gt;discordance&lt;/span&gt;**&lt;span style="line-height: 1.5;"&gt;.&lt;/span&gt;
 While psychoacoustic concordance is not a feature universal to all styles of music, it has been utilized significantly in Western music in the study of intonation. For instance, flexible-pitch ensembles operating within 12-EDO, such as barbershop quartets and string ensembles, will often adjust intonationally from the underlying 12-EDO reference to maximize the concordance of individual chords. Indeed, the entire history of Western tuning theory -- from meantone temperament, to the various Baroque well-temperaments, to 12-EDO itself, to the modern [[@xenharmonic/Regular Temperaments|theory of regular temperament]] -- can be seen as an attempt to reason mathematically about how to generate manageable tuning systems that will maximize concordance and minimize discordance.
@@ Line 201: / Line 203: @@
   The general workings of the human auditory system lead to a plethora of well-documented and sonically interesting phenomena that can occur when a musical chord is played:&lt;br /&gt;
 &lt;ul&gt;&lt;li&gt;The perception of partial &lt;strong&gt;timbral fusion&lt;/strong&gt; of the chord into one complex sound&lt;/li&gt;&lt;li&gt;The appearance of a &lt;strong&gt;virtual fundamental&lt;/strong&gt; pitch in the bass&lt;/li&gt;&lt;li&gt;Timbral &lt;strong&gt;beatlessness&lt;/strong&gt;, compared to mistunings of the chord in the surrounding area&lt;/li&gt;&lt;li&gt;The appearance of a quick fluttering effect sometimes known as &lt;strong&gt;periodicity buzz&lt;/strong&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
-All of these effects share two common characteristics for chords played with harmonic timbres:&lt;br /&gt;
+These effects do not always appear strictly in tandem with one another. For instance, Paul Erlich has noted that most models for beatlessness measure 10:12:15 and 4:5:6 as being identical, whereas the latter yields exhibits more timbral fusion and a more salient virtual fundamental than the former. However, suppose we want to come up with a combined measure for how often effects such as the above tend to occur. It is then useful to note that&lt;br /&gt;
-&lt;ul&gt;&lt;li&gt;&lt;span style="line-height: 1.5;"&gt;they tend to appear most strongly for those chords with large subsets that correspond to simple chunks of the harmonic series&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span style="line-height: 1.5;"&gt;the effects produced exhibit some degree of tolerance for mistuning&lt;/span&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+&lt;br /&gt;
-As the presence or absence of these effects tend to appear in tandem and are highly correlated with one another, we can speak of a general notion of the psychoacoustic &lt;strong&gt;concordance&lt;/strong&gt; of an interval - the degree to which effects such as the above will appear when an arbitrary musical chord is played. Additionally, chords which are very inharmonic often exhibit a quality known as psychoacoustic &lt;strong&gt;discordance&lt;/strong&gt;.&lt;br /&gt;
+&lt;br /&gt;
+&lt;ul&gt;&lt;li&gt;&lt;span style="line-height: 1.5;"&gt;effects such as these tend to appear most strongly for those chords with large subsets that correspond to simple chunks of the harmonic series&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span style="line-height: 1.5;"&gt;the effects produced exhibit some degree of tolerance for mistuning&lt;/span&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+&lt;span style="line-height: 1.5;"&gt;This enables us to speak of a general notion of the psychoacoustic &lt;/span&gt;&lt;strong&gt;&lt;span style="line-height: 1.5;"&gt;concordance&lt;/span&gt;&lt;/strong&gt;&lt;span style="line-height: 1.5;"&gt; of an interval - the degree to which effects such as the above will appear when an arbitrary musical chord is played. Additionally, chords which are very inharmonic often exhibit a quality known as psychoacoustic &lt;/span&gt;&lt;strong&gt;&lt;span style="line-height: 1.5;"&gt;discordance&lt;/span&gt;&lt;/strong&gt;&lt;span style="line-height: 1.5;"&gt;.&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
 While psychoacoustic concordance is not a feature universal to all styles of music, it has been utilized significantly in Western music in the study of intonation. For instance, flexible-pitch ensembles operating within 12-EDO, such as barbershop quartets and string ensembles, will often adjust intonationally from the underlying 12-EDO reference to maximize the concordance of individual chords. Indeed, the entire history of Western tuning theory -- from meantone temperament, to the various Baroque well-temperaments, to 12-EDO itself, to the modern &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Regular%20Temperaments" target="_blank"&gt;theory of regular temperament&lt;/a&gt; -- can be seen as an attempt to reason mathematically about how to generate manageable tuning systems that will maximize concordance and minimize discordance.&lt;br /&gt;